Exploring Convergence of the PageRank Algorithm

As part of learning more about the PageRank algorithm, I created a web app that lets you add/remove nodes and links, and see how this might impact the calculated PageRank values for small web systems. I have now also added the ability to watch how the power method converges (or not) to the PageRank vector for a web system. You can step forward or backward in the iteration process, as "stuff" moves amongst the pages each step. This can be particularly interesting in cases where the method does not converge, as you can (usually) see the stuff cycling through the system.

You click the "Explore Convergence" button to explore the convergence, and click the "Hide Convergence" button to return back to "normal mode".

Click the "Explore Convergence" button over there on the right to watch how the power method converges (or doesn't converge, if that be the case).

Once the "Explore Convergence" button is clicked, a few extra things related to the power method are shown on the screen near the top. Clicking the "Hide Convergence" button will hide this extra stuff, and show the final result of the iteration method once again.

By using the left/right arrows anywhere on the page (or by using the slider), you can step forward or backward through the power iteration method.

One thing that might stand out to you is how stuff will get sent to apparently "disconnected" pages as the method progresses. This is because - unless the damping factor is one - the PageRank algorithm forces every page to be connected to every other page in the web, although the "pipes" between the pages are very small.

The purpose of this page is to summarize in one place some of the interactive visualizations I have worked on. Most of these were built...

"When you start on your journey to Ithaca, then pray that the road is long, full of adventure, full of knowledge... Always keep Ithaca fixed in your mind. To arrive there is your ultimate goal. But do not hurry the voyage at all." (from "Ithaca", by C. P. Cavafy)